What is a complex number?

A complex number is a number that has both a real part and an imaginary part, expressed as $$a + bi$$ , where 'a' is the real part and 'b' is the imaginary part.

What is the square of an imaginary number?

The square of an imaginary number $$bi$$ is given by $$(bi)^2 = b^2i^2 = -b^2$$ .

How do you express a complex number in standard form?

A complex number is expressed in standard form as $$a + bi$$ , where 'a' is the real part and 'b' is the coefficient of the imaginary part.

What is the conjugate of a complex number $$a + bi$$ ?

The conjugate of a complex number $$a + bi$$ is $$a - bi$$ .

What is the modulus of a complex number $$a + bi$$ ?

The modulus of a complex number $$a + bi$$ is given by $$\sqrt{a^2 + b^2}$$ .

What is the argument of a complex number $$a + bi$$ ?

The argument of a complex number $$a + bi$$ is the angle formed with the positive real axis, calculated as $$\tan^{-1}(\frac{b}{a})$$ .

Simplify Imaginary Numbers Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an imaginary number?

Back

Tags

CCSS.HSN.CN.A.1

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.CN.A.1

3.

FLASHCARD QUESTION

Front

Back

5i.

4.

FLASHCARD QUESTION

Front

Back

7i.

5.

FLASHCARD QUESTION

Front

What is the imaginary unit 'i'?

Back

'i' is defined as the square root of -1, and it is used to represent imaginary numbers.

Tags

CCSS.HSN.CN.A.1

6.

FLASHCARD QUESTION

Front

How do you simplify a square root of a negative number?

Back

7.

FLASHCARD QUESTION

Front

What is the relationship between real numbers and imaginary numbers?

Back

Real numbers can be represented on a number line, while imaginary numbers are represented on a perpendicular axis, forming the complex plane.

Tags

CCSS.HSN.CN.A.1

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